A sifter of the general type described is known for example, from U.S. Pat. No. 4,296,864. In this publication the sifting chamber is formed by an annular space which is present between stationary air baffles arranged at the outlet end of a sifting air supply spiral and rotor blades. The material for sifting is delivered to the upper end face of the rotor, carried outwards and deflected into the sifting chamber through which it then passes downwards. Whereas the coarse material falls downwards out of the sifting chamber, the fine material is carried with the sifting air into the rotor and leaves the rotor together with the sifting air through the upper or lower end.